Shehata-etal-OE-2017-Passive-flow-control-for-aerodynamic-performance-enhancement-of-airfoil

67 Pages·2017·5.07 MB·English

1 Passive flow control for aerodynamic performance enhancement of airfoil
2 with its application in Wells turbine – under oscillating flow condition

3
4 Ahmed S. Shehata1, 2*, Qing Xiao 1, Khalid M. Saqr3, Ahmed Naguib2, Day Alexander 1
5
6 1) Department of Naval Architecture, Ocean and Marine Engineering, University of
7 Strathclyde, Glasgow G4 0LZ, U.K
8 2) Marine Engineering Department, College of Engineering and Technology,
9 Arab Academy for Science Technology and Maritime Transport, P.O. 1029 AbuQir,
10 Alexandria, EGYPT
11 3) Mechanical Engineering Department, College of Engineering and Technology,
12 Arab Academy for Science Technology and Maritime Transport, P.O. 1029 AbuQir,
13 Alexandria, EGYPT
14 * Corresponding Author: Ahmed S. Shehata,
15 E-mail address: [email protected]
16
17 ABSTRACT
18 In this work, the passive flow control method was applied to improve the performance
19 of symmetrical airfoil section in the stall regime. In addition to the commonly used first
20 law analysis, the present study utilized an entropy generation minimization method to
21 examine the impact of the flow control method on the entropy generation characteristics
22 around the turbine blade. This work is performed using a time-dependent CFD model of
23 isolated NACA airfoil, which refers to the turbine blade, under sinusoidal flow
24 boundary conditions, which emulates the actual operating conditions. Wells turbine is
25 one of the most proper applications that can be applied by passive flow control method
26 because it is subjected to early stall. Additionally, it consists of a number of blades that
27 have a symmetrical airfoil section subject to the wave condition. It is deduced that with
28 the use of passive flow control, torque coefficient of blade increases by more than 40%
29 within stall regime and by more than 17% before the stall happens. A significantly
30 delayed stall is also observed.
1
1 Keywords: Sinusoidal flow; Wells turbine; Passive flow control method; Entropy generation;
2 Stall regime; Large Eddy Simulation.
3 Nomenclature
A The total blade area ( m2)
c Blade chord (m)
𝐶 Drag force coefficient
𝐷
𝐶 Lift force coefficient
𝐿
𝐶 Torque coefficient
𝑇
D The fluid domain
𝐷 Suction slot diameter (m)
𝑠𝑠
f Cycle frequency (Hz)

F In-line force acting on cylinder (N)
D
G The filter function
KE Kinetic Energy (J)
𝐿 Suction slot location from leading edge in chord percentage %
𝑠𝑠
K Turbulent kinetic energy (J/kg)
Δp Pressure difference across the turbine (N/m2)
𝑅 Mean rotor radius (m)
𝑚
S Local entropy generation rate (W/m2K)
gen
S Global entropy generation rate (W/K)
G
𝑆 Mean strain rate (1/s)
𝑖𝑗
S Thermal entropy generation rate (W/m2K)
t
S Viscous entropy generation rate (W/m2K)
V
T Reservoir temperature (K)
o
2
𝑈 Moving frame velocity (m/s)
u Reynolds Averaged velocity component in i direction (m/s)
i
V Volume of a computation cell (m3)
V Instantaneous Velocity (m/s)
a
𝑉 Highest speed of axial direction (m/s)
𝑎𝑚
V Initial velocity for computation (m/s)
o
𝑉 Relative velocity (m/s)
𝑟
W The net-work transfer rate (W/s)
W Reversible work transfer rate (W/s)
rev
𝜂 The efficiency in first law of thermodynamics
𝐹
𝜂 The second law efficiency
𝑆
 Viscosity (kg/ms)
𝜇 Turbulent viscosity (N.s/m2)
𝑡
 Density (kg/m3)
∅̅ Flow coefficient
𝜔 Rotor angular speed (rad/s)
 
uu Reynolds stress tensor
i j
1
List of Abbreviations

CFD Computational Fluid Dynamics
NACA National Advisory Committee for Aeronautics
OWC Oscillating Water Column
2D Two Dimensional
3D Three Dimensional
2
3
3
1 1. Introduction
2 The techniques developed to maneuver the boundary layer, either for the purpose of increasing
3 the lift or decreasing the drag, are classified under the general heading of boundary layer
4 control or flow control. In order to achieve separation postponement, methods of flow control
5 lift enhancement and drag reduction have been considered. It is important to note that flow
6 control can be defined as a process used to alter a natural flow state or development path
7 (transient between states) into a more desired state (or development path; e.g. laminar,
8 smoother, faster transients) [1]. Moreover, it could be more precisely defined as modifying the
9 flow field around the airfoil to increase lift and decrease drag. This could be achieved by using
10 different flow control techniques such as blowing and suction, morphing wing, plasma
11 actuators, and changing the shape of the airfoil [2]. All the techniques essentially do the same
12 job, i.e. reduce flow separation so that the flow is attached to the airfoil and, thus, reduce drag
13 and increase lift. In regards to flow control techniques, they can be broadly classified as active
14 and passive flow control which can be further classified into more specific techniques [3]. The
15 terms “active” or “passive” do not have any clearly accepted definitions, but nonetheless are
16 frequently used. Typically, the classification is based on energy addition, either on the
17 possibility of finding parameters and modifying them after the system is built, or on the
18 steadiness of the control system; whether it is steady or unsteady. Such studies have
19 demonstrated that suction slot can modify the pressure distribution over an airfoil surface and
20 have a substantial effect on lift and drag coefficients [4-9]. A wide variety of different studies
21 have been conducted on flow control techniques. In actual fact, in 1904, Prandtl [10] was the
22 first scientist who employed boundary layer suction on a cylindrical surface to delay boundary
23 layer separation. The earliest known experimental works on boundary layer suction for wings
24 were conducted in the late 1930s and the 1940s [11-13]. Huang et al. [14] studied the suction
25 and blowing flow control techniques on a NACA0012 airfoil. The combination of jet location
26 and angle of attack showed a remarkable difference concerning lift coefficient as perpendicular
27 suction at the leading edge increased in comparison to the case in other suction situations.
28 Moreover, the tangential blowing at downstream locations was found to lead to the maximum
29 increase in the lift coefficient value. Rosas in [15] numerically studied flow separation control
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1 through oscillatory fluid injection, in which lift coefficient increased. The authors in [16]
2 examined the optimization of synthetic jet parameters on a NACA0015 airfoil in different
3 angles of attack to increase the lift to drag ratio. Their results revealed that the optimum jet
4 location moved toward the leading edge and the optimum jet angle incremented as the angle of
5 attack increased. The CFD method has been increasingly used to investigate boundary layer
6 control. Many flow control studies by CFD approaches [17-20] have been conducted to
7 investigate the effects of blowing and suction jets on the aerodynamic performance of airfoils.
8 The major challenge facing oscillating water column ocean energy extraction systems is to find
9 an efficient and economical means of converting flow kinetic energy to unidirectional rotary
10 motion for driving electrical generators [21-25], as seen in Figure 1. The energy conversion
11 from the oscillating air column [26, 27] can be achieved by using a self-rectifying air turbine
12 such as Wells turbine which was invented by A. A. Wells in 1976, see Figure 2 [28-33]. Wells
13 turbine consists of a number of blades that have symmetrical airfoil section. This airfoil section
14 under different conditions with various geometric parameters was investigated by other
15 researchers in consideration of improving the overall system performance. In order to achieve
16 this purpose, different methods were used, such as experimental, analytical and numerical
17 simulation. The main disadvantage of Wells turbine is the stall condition [34]. Aerodynamic
18 bodies subjected to pitching motions or oscillations exhibit a stalling behavior different from
19 that observed when the flow over a wing at a fixed angle of attack separates. The latter
20 phenomenon is referred to as static stall, since the angle of attack is fixed. In the case of a
21 dynamically pitching body, such as an airfoil with large flow rates and a large angle of attack,
22 the shear layer near the leading edge rolls up to form a leading-edge vortex which provides
23 additional suction over the upper airfoil surface as it convects downstream. This increased
24 suction leads to performance gains in lift and stall delay, but the leading-edge vortex quickly
25 becomes unstable and detaches from the airfoil. As soon as it passes behind the trailing edge,
26 however, the leading-edge vortex detachment is accompanied by a dramatic decrease in lift and
27 a significant increase in drag. This phenomenon is called dynamic stall. From Figure 3 it can be
28 noted that Wells turbine can extract power at low air flow rate, when other turbines would be
29 inefficient[35, 36]. Also, the aerodynamic efficiency increases with the increase of the flow
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1 coefficient (angle of attack) up to a certain value, after which it decreases. Thus, most of the
2 past studies aimed to 1) improve the torque coefficient (the turbine output) and 2) improve the
3 turbine behavior under the stall condition. In a number of previous studies [37-39], it was
4 concluded that the delay of stall onset contributes to improving Wells turbine performance.
5 This delay can be achieved by setting guide vanes on the rotor’s hub [37, 40, 41]. It was found
6 that a multi-plane turbine without guide vanes was less efficient (approximately 20%) than the
7 one with guide vanes. A comparison between Wells turbines having 2D guide vanes and 3D
8 guide vanes was investigated [42, 43] by testing a Wells turbine model under steady flow
9 conditions, and using the computer simulation (quasi-steady analysis. It demonstrated that, the
10 3D case has superior characteristics in the running and starting characteristics. Concerning
11 Wells turbine systems which operate at high pressure values, a multi plane (usually tow stage)
12 turbine configuration can be used. Such a concept avoids the use of guide vanes and, therefore,
13 the turbine would require less maintenance and repairs [37]. The performance of a biplane
14 Wells turbine is dependent on the gap between the planes as it is shown in [37]. A gap-to-chord
15 ratio between the planes of 1.0 was recommended. Experimental results in [44] showed that
16 the use of two twin rotors rotating in the opposite direction to each other was an efficient means
17 of recovering the swirl kinetic energy without the use of guide vanes. The overall performance
18 of several types of Wells turbine design have been investigated in [45] and, a semi-empirical
19 method for predicting the performance has been used in [46]. Similar comparisons were
20 undertaken using experimental measurement in [47]. It can be observed that the contra-rotating
21 turbine had an operational range which was similar to that of the monoplane turbine with guide
22 vanes and it achieved similar peak efficiency as well. However, the flow performed was better
23 than the latter in the post-stall regime. In order to improve the performance of the Wells
24 turbine, the effect of end plate on the turbine characteristics has been investigated in [48, 49].
25 Using an experimental model and a CFD method it was shown that the optimum plate position
26 was a forward type. The peak efficiency increases approximately 4% as compared to the Wells
27 turbine without an endplate. The calculations of the blade sweeps for the Wells turbine with a
28 numerical code by [50] and experimentally with quasi-steady analysis in [51]. As a result, it
29 was concluded that the performance of the Wells turbines was influenced by the blade sweep
30 area.
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1 Exergy analysis is performed using the numerical simulation for steady state biplane Wells
2 turbines [52] where the upstream rotor has a design point second law efficiency of 82.3%
3 although the downstream rotor second law efficiency equals 60.7%. The entropy generation,
4 due to viscous dissipation, around different 2D airfoil sections for Wells turbine was recently
5 examined by the authors in [53, 54]. When Reynolds number was increased from 6×104 to
6 1×105 the total entropy generation increased more than two folds for both airfoils
7 correspondingly. However, when Reynolds number was increased further to 2×105, the total
8 entropy generation exhibited unintuitive values ranging from 25% less to 20% higher than the
9 corresponding value at Reynolds number = 1×105. The efficiency for four different airfoils in
10 the compression cycle is higher than the suction cycle at 2 degree angle of attack. Although,
11 when the angle of attack increases, the efficiency for the suction cycle increases much more
12 than the compression one. This study suggested that a possible existence of critical Reynolds
13 number for the operating condition at which viscous irreversibilities takes minimum values. A
14 comparison between total entropy generation of a suggested design (with variable chord) and a
15 constant chord of Wells turbine was presented in [55]. The detailed results demonstrate an
16 increase in static pressure difference around a new blade and a 26.02 % average decrease in
17 total entropy generation throughout the full operating range. Most of the researchers studied the
18 performance of different airfoils design and different operational conditions where analyzing
19 the problem was only based on the parameter of first law of thermodynamics. In order to form a
20 deeper understanding, it is necessary to look at the second law of thermodynamics since it has
21 shown very promising result in many applications, such as wind turbine in [56-61], and gas
22 turbine in [62-67].
23 Wells turbine consists of a number of blades that have symmetrical airfoil section. This airfoil
24 section under different conditions with various geometric parameters was investigated by other
25 researchers to improve the overall system performance. Different methods were used to achieve
26 this purpose, such as experimental, analytical and numerical simulation. In this work the CFD
27 analysis is used to investigate and analyze the flow around the isolated NACA airfoil, which
28 refers to the turbine blade, under sinusoidal flow boundary conditions, which emulates the
29 actual operating conditions. The force coefficients, such as torque coefficient and the entropy
7
1 generation value, are calculated and compared under different conditions with various design
2 parameters by analyzing the flow around the airfoil section using CFD software, where the
3 force coefficients are referring to the first law analysis and the entropy generation value is
4 referring to the second law analysis. The objective of the present work is to demonstrate that
5 the performance of airfoil section, which refers to the Wells turbine blade at stall and near-stall
6 conditions, can be radically improved by using passive flow control method such as suction or
7 blowing slot. Therefore, a typical slot is created in the airfoil section, normal to the chord, and
8 due to the pressure difference between the two surfaces. Consequently, a suction effect occurs
9 which delays the stall. Accordingly, there is no need to generate any specific active suction or
10 blowing within the airfoil or the slot. Along with this design, there are two new aspects here.
11 The first is improving the performance of airfoil section for Wells turbine in near-stall
12 conditions. The second is to study the effect of slot in oscillating (i.e. sinusoidal) flow, which is
13 newly compared to the unidirectional flow as in aerodynamics applications. Apart from that, an
14 entropy generation minimization method is used to conduct the second-law analysis as recently
15 reported by the authors in [53, 54]. An investigation on the entropy generation, due to viscous
16 dissipation, around turbine airfoils in two-dimensional unsteady flow configurations, will be
17 carried out. In reference to the literature, no specific unsteady CFD study of the slot effect with
18 sinusoidal flow on the entropy generation rate has been performed for airfoil section of Wells
19 turbine.
20 2. Mathematical Model and Numerical Approach
21 The governing equations employed for Large Eddy Simulation (LES) are obtained by filtering
22 the time-dependent Navier-Stokes equations. The filtering process effectively filters out eddies
23 whose scales are smaller than the filter width or grid spacing used in the computations. The
24 resulting equations thus govern the dynamics of large eddies. A filtered variable (denoted by an
25 over-bar) is defined by [68]:
26 𝜙 (𝑥) = ∫ 𝜙(𝑥′)𝐺(𝑥,𝑥′)𝑑𝑥′ (1)
𝐷
8
1 where D is the fluid domain, and G is the filter function that determines the scale of the
2 resolved eddies. In FLUENT, the finite-volume discretization itself implicitly provides the
3 filtering operation[69]:
4 𝜙 (𝑥) = 1∫ 𝜙(𝑥′)𝑑𝑥′, 𝑥′ ∈ 𝑉 (2)
𝑉 𝑉
5 where 𝑉 is the volume of a computational cell. The filter function, G (x, x'), implied here is
6 then
1⁄𝑉 𝑓𝑜𝑟 𝑥′ ∈ 𝑉
7 𝐺 (𝑥, 𝑥′) = { (3)
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
8
9 The LES model will be applied to essentially incompressible (but not necessarily constant-
10 density) flows. By filtering the incompressible Navier-Stokes equations, one obtains [70]
𝜕𝜌 𝜕𝜌𝑢
11 + 𝑖 = 0 (4)
𝜕𝑡 𝜕𝑥
𝑖
12 𝜕 (𝜌𝑢 ) + 𝜕 (𝜌𝑢 𝑢 ) = 𝜕 (𝜇𝜕𝑢𝑖 ) − 𝜕𝜌 − 𝜕𝜏𝑖𝑗 (5)
𝑖 𝑖 𝑗
𝜕𝑡 𝜕𝑥 𝜕𝑥 𝜕𝑥 𝜕𝑥 𝜕𝑥
𝑗 𝑗 𝑗 𝑖 𝑗
13 Where 𝜏 is the sub-grid-scale stress defined by
𝑖𝑗
14 𝜏 = 𝜌𝑢 𝑢 − 𝜌𝑢 𝑢 (6)
𝑖𝑗 𝑖 𝑗 𝑖 𝑗
15 The sub-grid-scale stresses resulting from the filtering operation are unidentified, and require
16 modeling. The majority of sub-grid-scale models are eddy viscosity models of the following
17 form [71]:
1
18 𝜏 − 𝜏 𝜎 = −2𝜇 𝑆 (7)
𝑖𝑗 𝑘𝑘 𝑖𝑗 𝑡 𝑖𝑗
3
19 Where 𝑆 is the rate-of-strain tensor for the resolved scale defined by:
𝑖𝑗
20 𝑆 = 1(𝜕𝑢𝑖 +𝜕𝑢𝑗) (8)
𝑖𝑗
2 𝜕𝑥 𝜕𝑥
𝑗 𝑖
21 and 𝜇 is the sub-grid-scale turbulent viscosity, which the Smagorinsky-Lilly model is used for
𝑡
22 it [72]. The most basic of sub-grid-scale models for “Smagorinsky-Lilly model” was proposed
23 by Smagorinsky [73] and was further developed by Lilly [74]. In the Smagorinsky-Lilly model,
24 the eddy viscosity is modeled by:
25 𝜇 = 𝜌𝐿2 |𝑆| (9)
𝑡 𝑠
9
1 where 𝐿 is the mixing length for sub-grid-scale models and |𝑆| = √2𝑆 𝑆 . The 𝐿 is
𝑠 𝑖𝑗 𝑖𝑗 𝑠
2 computed using:
3 𝐿 = min (𝑘𝑑,𝐶 𝑉1⁄3) (10)
𝑠 𝑠
4 Where 𝐶 is the Smagorinsky constant, 𝑘 = 0.42, 𝑑 is the distance to the closest wall, and 𝑉 is
𝑠
5 the volume of the computational cell. Lilly derived a value of 0.23 for 𝐶 from homogeneous
𝑠
6 isotropic turbulence. However, this value was found to cause excessive damping of large-scale
7 fluctuations in the presence of mean shear or in transitional flows. 𝐶 = 0.1 has been found to
𝑠
8 yield the best results for a wide range of flows.
9
10 For the first law of thermodynamics, the lift and drag coefficient 𝐶 and 𝐶 are computed from
𝐿 𝐷
11 the post processing software. The average value for lift and drag coefficient was used to
12 calculate one value for torque coefficient for each angle of attack. Afterwards, the torque
13 coefficient can then be expressed as [39, 46, 75]:
14 𝐶 = (𝐶 𝑠𝑖𝑛 − 𝐶 cos ) (11)
𝑇 𝐿 𝐷
̅
15 The flow coefficient 𝜙 relating tangential and axial velocties of the rotor is difined as
16 𝜙̅ = 𝑉𝑎 (12)
𝜔 ∗𝑅𝑚
17 where the  angle of attack equal to
18 𝛼 = 𝑡𝑎𝑛−1 𝑉𝑎 (13)
𝜔 𝑅𝑚
19 and the torque as:
20 𝑇𝑜𝑟𝑞𝑢𝑒 = 1𝜌(𝑉 2 +( 𝜔 𝑅 )2) 𝐴𝑅 𝐶 (14)
𝑎 𝑚 𝑚 𝑇
2
21 the efficiency in the first law of thermodynamics (𝜂 ) is defined as:
𝐹
𝑇𝑜𝑟𝑞𝑢𝑒∗ 𝜔
22 𝜂 = (15)
𝐹
𝛥𝑃∗𝑄
23 The transport equations of such models can be found in turbulence modeling texts such as [76].
24 The second law of thermodynamic defines the network transfer rate W as [77]:
25 W W T S (16)
rev o gen
10